**PROJECT
PN-III-P4-ID-PCE-2016-0649**

**PARALLEL
THEORETICAL STUDY OF THE TWO COMPONENTS OF THE PROMPT FISSION
NEUTRONS: DYNAMICALLY RELEASED AT SCISSION AND EVAPORATED FROM FULLY
ACCELERATED FRAGMENTS **

**Supported by CNCS-UEFISCDI contract
no 194/2017, hosted by Horia Hulubei National Institute for Physics
and Nuclear Engineering, Bucharest.**

**ABSTRACT**

**The
discovery of the fission process and its explanation was one of the
most important advances in nuclear physics of the last century. It
was not only important for the fundamental understanding of heavy
nuclei but also for the applications. The prompt fission neutrons
(PFN) are mandatory in producing nuclear energy since they make the
chain reaction of fissile nuclei possible. Their properties are
essential for the design of nuclear power plants, the safe operation
of nuclear reactors, the handling of nuclear waste and the
investigation of next-generation reactor systems and fuel cycles.**

**A
detailed theoretical study of PFN properties is therefore of utmost
importance and this is the context in which the present project takes
place. The main characteristics of the PFN (an emission along the
fission axis and an exponentially decreasing energy spectrum) led to
the first guess about their origin: they are evaporated by the
fission fragments when these fragments are fully accelerated. The
emission is supposed to occur relatively long after the division of
the fissioning system into two fragments. **

**However,
some observed PFN characteristics suggest the existence of an earlier
(e.g. around scission) neutron emission of a different origin. This
is due to the rapidly changing neutron-nucleus potential during the
scission process. **

**The
goal of this project is to provide elements for answering the
important question of the nature and relative abundance of the two
components of the prompt fission neutrons (emitted during scission
and evaporated from accelerated fragments).**

**A
recent dynamical scission model will be used to calculate the
characteristics of the neutrons dynamically released during the
scission process, i.e., during the rupture of the neck connecting the
nascent fragments and the absorption of the neck stubs by the primary
fragments. Three categories of observables will be tackled: **

**1)
The scission neutron multiplicity. Its dependence on the fragments'
mass ratio and on the model assumptions will be studied.**

**2)
The angular distribution of the scission neutrons with respect to the
fission axis. Its dependence on the mass ratio, on the projection of
the angular momentum on the nuclear axis and on the fragments'
deformation at scission will be investigated.**

**3)
The scission neutron energy spectrum. Its shape and its average value
will be studied as a function of the mass asymmetry and of the model
assumptions. Additional information on the time evolution of the
emission process will be obtained by calculating the time dependent
decay rate.**

**The
old hypothesis that fission neutrons are evaporated from fully
accelerated fragments will be also investigated. For this we will
employ an advanced version of the Hauser-Feshbach statistical
approach combined with a Monte-Carlo sampling of initial conditions.
The same observables will be estimated with both methods and the
results compared. When possible, the two models will be confronted
with experimental data.**

**REPORT
2017 (in English)**

**REPORT
2018 (in English)**

**REPORT
2019 (in English)**

**PUBLICATIONS
IN THE FRAME OF THE PROJECT - PUBLICATII IN CADRUL PROIECTULUI**

**(UPDATED
NOVEMBER 2019 – ACTUALIZARE NOIEMBRIE 2019)**

**PUBLICATIONS**

[1] Parallel theoretical study of the two components of the prompt fission neutrons: dynamically released

at
scission and evaporated from fully accelerated fragments, N.Carjan,
M.Rizea, P.Talou, *EPJ Web of Conferences* **146**,
art.no.04002, p.1-6 (2017)

[2]
Fourier transform of single-particle wave functions in extremely
deformed nuclei: towards the momentum distribution of scission
neutrons, M.Rizea, N.Carjan, *EPJ Web of Conferences ***169,
***art.no.00020 (2018)*

[3]
Charge polarization and the elongation of the fissioning nucleus at
scission, C.Ishizuka, S.Chiba, N.Carjan, *Romanian
Reports in Physics ***70***,
202 (2018) *

[4]
Structures in the energy distribution of the scission neutrons: finite
neutron-number effect, N.Carjan, M.Rizea, *Physical
Review C 99, 034613 (2019)*

[5]
Fission of superheavy nuclei: Fragment mass distributions and their
dependence on excitation energy, N.Carjan, F.A.Ivanyuk, Yu.Ts.Oganessian, *
Physical Review C 99, 064606 (2019)*

**CONFERENCES**

[1]
Gross structures in the scission neutrons angular and energy
distributions, N.Carjan, M.Rizea, in *Theory-4: Nuclear Fission
Dynamics and the Emission of Prompt Neutrons and Gamma Rays*, June
20-22, 2017, Varna, Bulgaria

[2]
Fourier transform of single-particle wave functions in extremely
deformed nuclei: towards the momentum distribution of scission
neutrons, M.Rizea, N.Carjan, in *Theory-4: Nuclear Fission Dynamics
and the Emission of Prompt Neutrons and Gamma Rays*, June 20-22,
2017, Varna, Bulgaria

[3] Predictions
of fission fragments mass distributions for super-heavy elements,
N.Carjan, in *Spontaneous
and induced fission of very heavy and super-heavy nuclei,*
April
9-13, 2018, Trento, Italy and *EXON-2018,
IX International Symposium on Exotic Nuclei,*
September
10-15, 2018, Petrozavodsk, Russia

[4] Acceleration
induced neutron emission in heavy nuclei, N.Carjan, M.Rizea in
*ISINN-26,
26*^{th}*International
Seminar on Interaction of Neutrons with Nuclei, *May
28 – June 1, Xi'an, China
*and
Fifth Joint Meeting of the Nuclear Physics Division of the American
Physical Division of the American Physical Society and the Physical
Society of Japan, *October
23-27, 2018, Hawaii, USA

[5]
Multiplicity of Scision Neutrons from Density Functional Scission Dynamics,
N.Carjan, I.Stetcu, M.Rizea, A.Bulgac, in *Theory-5: Nuclear Fission Dynamics
and the Emission of Prompt Neutrons and Gamma Rays*, September 24-26,
2019, Barga, Italy

**PROJECT
TEAM**

Nicolae Carjan

Margarit Rizea

**PROJECT
OBJECTIVES**

**1. The shape of the scission
neutrons (SN) energy spectrum**

In the frame of the dynamical scission model we calculated for 236-U the distribution of the average energy of each emitted SN and compared it to the general trends of the measured spectrum. A good agreement was found. It is however necessary to calculate not only the average energy but the whole SN spectrum. For this we need to calculate the Fourier transforms of the unbound parts of the wave packets that describe the SN immediately after scission. These will provide the SN momentum distribution from which one can derive the kinetic energy distribution. It is expected that at low and high kinetic energies the SN spectrum differs from the evaporation spectrum, leading to an opportunity to distinguish between the two components of the PFN.

**2. The time dependent decay rate**

This calculation will reveal the time evolution of the SN emission process. It will answer questions such as: a) how long it takes before 10, 50 and 90% the neutrons released during scission leave the fissioning system and b) is the decay exponential or oscillatory? Although the two components of the PFN are separated in time, their tails may overlap. In this region a competition between scission and evaporated neutrons takes place: a possibility that has not been evoked so far.

**3. Dependence of the SN energy and
angular distributions on the quantum number Ω
representing the projection of the angular momentum of the neutron on
the symmetry (nuclear) axis**

For this we will estimate the relative contribution of each set of neutron eigenstates (defined by Ω)

to these distributions. Knowing to which angular and energy domain each Ω-value contributes most, one could experimentally select PFN with more or less well defined quantum number. This possibility is unique (not available from other sources).

**4.
Dependence of the SN multiplicity on the mass asymmetry for 236-U
and 252-Cf**

The SN multiplicity will be calculated as a function of the mass ratio A-light/A-heavy and compared with total (summed over the light and the heavy fission fragments) PFN multiplicities recently measured during the rections 235-U(nth,f) and 252-Cf(sf).

**5. The comparison of
the results obtained with the two hypotheses about the origin of the
PFN**

It will be made on the mass-asymmetry dependence of the angular and kinetic energy distributions. Calculations will be made for different mass asymmetries of 236-U using both our dynamical scission model and the most advanced version of the traditional evaporation model. These predictions will be confronted with recent measurements of the same quantities.

**6. The influence of
the parameters of the dynamical scission model**

These parameters are the neck radius of the just before scission configuration and the distance between the inner tips of the nascent fragments immediately after scission. They define the length of the non-adiabatic transition during scission. We will choose three situations that correspond to a short, an intermediate and a long jump respectively.

**PROGRESS
SUMMARY **

**2017**- The Fourier transform of
single particle wave functions in cylindrical coordinates is applied
to the study of neutrons released during scission. We propagate the
neutron wave packets in time through the bi-dimensional time
dependent Schrodinger equation with time dependent potential. We
separate the parts of these wave packets that are in the continuum
and calculate their Fourier transforms at different times:
immediately after scission (T = 10^{-22} sec) and at several
intervals afterwards (until T = 50 x 10^{-22} sec). The momentum
distributions corresponding to these Fourier transforms are then
estimated. The evolution of these distributions in time provides an
insight into the separation of the neutron from the fissioning system
and asymptotically gives the kinetic energy spectrum of that
particular neutron.

**2018**- We have
determined the time-dependent decay rate for the neutrons leaving a
sphere around the nucleus. This provides additional informations
about the evolution of the emission process. Thus, it is evaluated
the time necessary for different amount of neutrons to be released
from the fissioning nucleus and it is shown up the character of the
scission neutron emission (exponential or oscillatory). The
dependence of the decay rate on the quantum number $\Omega$ and on
the radius of the sphere around the nucleus was also studied. The
scission neutron angular distribution and the energy spectrum have
been calculated for different time intervals and for several $\Omega$
values as well. Relevant features of the two types of neutrons (of
scission and evaporated) are discussed.

**2019**- We have studied
the dependence of the scission neutron multiplicity on the mass ratio of
the fission fragments in the case of 236U and 252Cf. The multiplicities
are calculated both in the sudden approximation and in the dynamical model.
We have compared the results, namely the angular and the energy distribution,
obtained in the frame of the two hypotheses with respect to the origin of
the prompt neutrons of fission (evaporated or emitted at scission).
Several tests have been performed on the influence of the dynamical
model parameters: the minimal radius before scission and the distance
between the interior surfaces of the fragments after scission. Comparisons
with experimental data are also included.